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# Ordering 4-digit numbers

Alignments to Content Standards: 4.NBT.A.2

## Task

1. Arrange these numbers in increasing order, beginning with the least. $$2400 \qquad 4002 \qquad 2040 \qquad 420 \qquad 2004$$

2. Arrange these numbers in decreasing order, beginning with the greatest. $$1470 \qquad 847 \qquad 710 \qquad 1047 \qquad 147$$

## IM Commentary

It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.

## Solution

1. $$420 \qquad 2004 \qquad 2040 \qquad 2400 \qquad 4002$$ We know that 420 is less than any four-digit number. Of the numbers 2004, 2040, and 2400, 2004 is the least, and 2400 is the greatest, since four ones are less than four tens, and four tens are less than four hundreds. 4002 is the greatest number since it contains four thousands, and the other three four-digit numbers contain less than three thousands.

2. $$1470 \qquad 1047 \qquad 847 \qquad 710 \qquad 147$$ We know that 1470 and 1047 are greater than the three three-digit numbers, since 1470 and 1047 are both greater than one thousand, and the three-digit numbers are less than one thousand. 1470 is greater than 1047 because 1470 contains one thousand and four hundreds, while 1047 contains one thousand and less than one hundred. We know that 847 is greater than 710 because 847 contains eight hundreds, and 710 contains less than eight hundreds. 710 is greater than 147 because 710 contains seven hundreds, and 147 contains less than two hundreds.

## Comments

#### Elizabeth says:

over 3 years

I think that this activity only covers half if not less of the standard. Yes, the students are comparing the four digit numbers, but I do not see any evidence that the teacher wanted the students to use the symbols specified in the standard: >, <, or =. According to the standard, students are required to compare the numbers using the symbols, and not compare them just to compare them. This is a great idea, but it doesn't match what the state requires.

#### Cam says:

over 3 years

Hi mseruch,

No disagreement here. It's rare that we try to cover the full range of concepts inherent in one standard with a single task. Some standards are so direct that a single task does indeed suffice, but others (like this one) have such a broad scope that it's best to think of covering it via a collection of tasks, each of which might cover only one piece.

Thanks for the comment!

#### Adam Battle says:

almost 5 years

This task exceeds the parameters of the standard. Students should only be comparing two multi-digit numbers in Grade 4.

#### Cam says:

almost 5 years

Isn't sorting a list just repeatedly comparing two numbers? First, students compare 420 to each of the other entries in the list, and deduce that it is smaller than each of them. Then repeat.

#### Adam Battle says:

almost 5 years

I agree that ordering a list of numbers is done by repeatedly comparing two numbers, but I do not think this task is aligned to this particular standard. Wouldn’t the standard say, “Compare and order three or more multi-digit numbers…” if students were supposed to complete a task like this? This seems like a great task for students who require differentiation, but I’d be hesitant to use it to assess students.

#### Cam says:

almost 5 years

I would argue no. I don't think there is any instance of any standards anywhere which, for example, separate the abilities of "adding two numbers together" and "adding three numbers together." Instead, it's understood that we understand the sum of multiple numbers as repeatedly applying our knowledge of adding two numbers. I think it's the same with this task. That said, it's possible you have a point about assessment -- not all legitimate illustrations of a standard are reasonable for assessment!

#### kdallavalle says:

over 6 years

This task is reasonable for a fourth grade student,